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Fiscal policies and the integrated world stock market
Journal of International
Economics 29 (1990) 109-122. North-Holland
FISCAL POLICIES
AND THE INTEGRATED MARKET
WORLD
STOCK
Assaf RAZIN* Tel-Aviv Unicersity, Tel Aviv 69978. Israel
Received September 1988, revised version received December 1989 The paper develops a two-country stochastic model of an integrated world stock market in order to address issues concerning the effects of tax and spending policies on savings, asset portfolios, and stock-market valuations. General conditions for government-finance neutrality under uncertainty are derived and the characteristics of the international transmission of uncertain future spending policies are spelled out. They are shown to depend precisely on a transfer-problem criterion involving the government and the private-sector propensities to spend in different states of nature and on the cross-country correlations between shocks to productivity and public spending.
1. Introduction
This paper develops a two-country stochastic general-equilibrium model of the world economy to address issues concerning the effects of fiscal policies on the international allocation of consumption, saving, and risk. The analytical framework is used to study the effects of government spending and tax policies on private-sector consumption, spending, and asset portfolios. The recent large swings in security prices that have taken place simultaneously throughout the OECD stock markets indicate the close international links existing among various stocks as a result of the integration of the world capital markets. They motivate the assumption of an integrated world stock market. The dynamic effects of fiscal policies on savings and investment have been the subject of a large body of recent research. Examples of such research in a closed-economy framework are Barro (1981) and Blanchard (1985), and examples in an open-economy framework are Buiter (1986), Frenkel and Razin (1985, 1987a, 1987b) and Persson (1985). This line of research, emphasizing intertemporal considerations, has been confined, however, to a full-certainty environment in which private-sector behavior is governed by *This is a revision of the NBER working paper no. 2398 (1987). I wish to thank Elhanan Helpman, Torsten Persson and Lars Svensson for useful comments. Partial tinancial support was provided by the Foerder Institute for Economic Research, Tel-Aviv University. 0022-1996/90/$03.50 0 1990-Elsevier
Science Publishers B.V. (North-Holland)
110
A. hrin,
integrated
world sock market
perfect foresight. The open-economy macroeconomic analysis under certainty focused mainly on the international and intertemporal allocation of consumption and investment and their manifestations in trade imbalances. In such a framework the terms of trade and the world rate of interest are the main channels through which fiscal policies in one country are transmitted to the rest of the world. The present paper extends the analysis to stochastic environments in which the main channel of transmission is the integrated world stock market. The extension of the international-intertemporal framework to stochastic environments is done here by specifying a stock-market model as in Diamond (1967), Helpman and Razin (1978) and Lucas (1978). A recent application of the model to international trade in assets is contained in Svensson (1988). The paper is organized in the following manner. In section 2 we set out the stochastic-intertemporal analytical framework. Section 3 considers the issue of the government-finance neutrality and section 4 contains the analysis of spending policies in the case of complete markets for risk sharing. In the context of incomplete markets, sections 5 and 6 investigate how the pro- and counter-cyclical behavior of government spending affects the stock market valuation of equities. The analysis highlights the role played by the correlations between the country-specific shocks and government spending shocks in the international transmission of fiscal policies. Section 7 contains concluding remarks. The appendix, which follows the text, includes algebraic derivations of the key characteristics of the asset-demand functions under uncertainty. 2. An intertemporal
stochastic model
Consider a two-period nonmonetary model of an open economy producing and consuming a single aggregate tradable good.’ The economy is endowed with a sequence of outputs, O,Y,, and B,(y) Y,, where subscripts zero and one designate the corresponding periods indexed by the state of nature, y. There are S possible states of nature, the quantities O,Y, and Y, are predetermined, and O,(y) is a productivity coefficient corresponding to the state of technology, ~=1,2 ,..., S. Similarly to Helpman and Razin (1978), let q be the price of a unit of real equity [a security which pays O(y) units of output in state 71 issued by the representative home firm, in terms of units of the aggregate consumption good. Home firms produce Yi units of these equities and their (gross) stock market value is equal to q- Y,. An asterisk denotes foreign variables. Accordingly, foreign firms produce the sequence O,*Y,*and O:(y) YT in periods zero and one, respectively; the price of a unit of foreign ‘The present model is a two-period one-good version of the model developed by Helpman and Razin (1978, ch. 11). Labor income is contained in the endowment BY. Fixed return bonds are introduced later, in section 5.
A. Razin, lntegrated
world stock market
111
real equity is denoted by q* and the stock-market value of foreign firms is equal to q* . YT. The domestic private-sector budget constraints are: &0 + q2,,l + qz;ci = qz,,, + q*z;O
+
oOzHO
+
@z;l;O
-
rO,
c”l(‘r’)=el(Y)zH1 +e:(;t)ztl - Tl(‘i).
(1)
(2)
In eqs. (1) and (2), CHOand C,,(y) denote first- and (state-y) second-period consumption and zHr and z& denote the shares of stocks issued by home and foreign firms in period t (t=O, 1). The productivity parameters, 8, and OF, indicate the amount of dividends, per share, paid by domestic and foreign firms, respectively, and T, denotes lump-sum taxes in period t (t = 0,l). In eq. (1) disposable income is equal to current dividends from the historically given portfolio (zno, z*no), plus the market value of this portfolio net of taxes, To. Income is spent on consumption, CHO, and on the new portfolio, (z H1,z;cIi). Second-period disposable income, specified in eq. (2), is derived from dividends on the pre-existing portfolio (net of taxes), but includes no resale value of stocks and no acquisition of new stocks, since this is the last period. Let u(C,,) and M(G,) be concave von Neumann-Morgenstern private and public components of the representative individual utility function, respectively, and let 6 denote the corresponding subjective discount factor. The expected utility is:
u=4&o)
+
~EuCCHI
(r)l+ WGo) + dEM(G, (Y)),
(3)
where E is the expectation operator. The consumption-portfolio choice problem is to maximize the private component of the expected utility function [eq. (3)], given common beliefs about the probability distribution of states of nature and subject to the budget constraints [eqs. (1) and (2)]. Given its own resources (through taxes and borrowing), G, the government, chooses Go and G, so as to maximize the public component of the expected utility function.
3. Neutrality of government finance To put aside issues of government finance and concentrate on spending policies in the subsequent analysis, we specify in this section conditions for a benchmark case in which government finance has no real consequence. Observe that the consolidated private-sector budget constraint [derived from eqs. (1) and (2)] is:
112
A. Razin, Integrated
It is evident
maintains the return on what may be called the ‘tax asset’ (the claim of government on private sector income) are proportional to the returns on the domestic security, state by state. Thus, the government finance activities effectively introduce no new security into the market. Simply stated, the government raises current-period taxes and use the proceeds to buy domestic equities, while in the next period state-dependent dividend revenue replaces taxes as a source of government finance. These financial transactions have no effect on the private sector. Conditions for government-finance neutrality can be stated as a proposition: (-)T,(y)/T,,
from
eq. (4) that
world stock market
any
tax-shift
policy
that
=O,(y)/q must be neutral. If tax policies fulfill this condition,
Proposition. The claim of the private sector on taxes can be viewed as a negative ‘asset’. Whether or not tax-shift policies are relevant depends on whether the induced distribution of returns on this ‘asset’ is spanned by the equilibrium returns on the prevailing assets.
4. Spending, international allocation of risk, and stock price valuations To highlight the effects of government spending on the international allocation of risk, and specifically on the relative price of the domestic security (in terms of the foreign security), we assume now that markets are complete. In the present context, since there are only two securities, this assumption implies that there exist two states of nature (0 and 1). Maximization of the private component of the expected utility yields: R(o)u’(o)e*(o) + K(l)u’( l)e*( 1) -* n(o)u’(o)e(o) + n( l)u’( l)e( 1)
’
(5)
where 4* is the relative price of the foreign security in terms of the domestic security. We denote the ratio of the price of a state-one contingent good, P,, to a state-zero contingent good, P,, by p. Then, as usual, in equilibrium the marginal rate of substitution is equal to the relative price. That is,
MU’
---c
?r(O)u’(O) p.
Eqs. (5) and (6) imply the following relationship between p and 4*:
(6)
A. Razin, lntegrated
world
stock market
,rlopc
1 AG(l)
=
.IPG(l)/MPG(O)
B(l)Y+ Z(l)Y.
OH
/
”
stopen
MPC(l)/MPC(O),
Fig. 1. The effect of a rise in government
e*(o)+Pe*u)=q_* w+Pf%l)
’
ll(O)Y
+ O’(O)Y’
spending
on the relative state-contingent
price.
(7)
Accordingly,
(8)
Similar conditions, with the same prices, hold for the foreign country. The equilibrium in the world economy is portrayed by the Edgeworth box in fig. 1. The horizontal axis measures world output in state zero [e(O) Y +0*(O) Y*] and the vertical axis measures the corresponding output in state one [0( l)Y+ 0*( l)Y*]. The international distribution of claims to world output is specified by the point E. As usual, quantities pertaining to the home country are measured from the point OH as the origin, and quantities pertaining to the foreign country are measures from point OF as the origin. The equilibrium obtains at point A, where the slope of the domestic and foreign indifference curves are both equal to the relative price, p. Using eq. (7) we can also derive the equilibrium relative price of the foreign security, $+.
114
A. Razin,
Integrated
world
stock market
The government propensity to spend in the first and second states is determined by maximizing the public component of the expected utility function, M(G0)+6~(0)-M(G,(O))+&( l)M(G,( l)), subject to the budget constraint G,+P,,G,(O)+P,G,( l)=G, where G denotes the present value of the tax revenue. Optimization yields the endogenously determined propensities to spend for the government, which depend on the probabilities (the x’s), on the relative price (p), and on the government resources (G).’ As in Frenkel and Razin (1987b), the basic criterion determining the effect of a rise in government spending on the relative price of goods involves a comparison between the ratio of government marginal propensities to spend, MPG(l)/MPG(O) [where MPG(i) is the government propensity to spend in state i] and the corresponding ratio of the domestic private sector propensities to consume, MPC(l)/MPC(O) [where MPC(i) denotes the privatesector marginal propensity in state i]. If the government propensity to spend exceeds the private-sector propensity to consume in state one, the rise in government spending and the corresponding fall in the disposable income of the domestic private sector create an excess demand for state-one goods and an excess supply of state-zero goods. As a result p rises. If, on the other hand, the government propensity falls short of the corresponding privatesector propensity, the equilibrium relative price, p, must fall. This is indicated in fig. 1 by the diminished size of the box. In the borderline case which is shown in the figure, the relative propensities of the public and the private sectors are equal. The new equilibrium following the rise in government spending obtains at point B with no change in marketclearing prices. In this case there is no change in the relative price of the domestic security [see eq. (8)]. However, if the public-private propensity configuration is such that state-
one relative price, p, goes up, and if the domestic economy is relatively more productive in that state, the relative price of the domestic security must rise [as indicated by eq. (8)] and vice versa.
5. Spending and international allocation of risk with incomplete markets To highlight the effects of spending policies in the case of incomplete markets we abstract now from issues of government finance assuming that the government runs a balanced budget [G,= T,, G,(y) = T,(y)]. From the maximization of the expected utility [eq. (3)] subject to the budget con-
‘If, for example, the utility function is logarithmic, the ratio of the marginal propensity to spend in state one to the corresponding propensity in state zero, [~G,(~)/c~G]/[X,(O)/ZG], is equal to probability
[n(i)/x(O)p]. Thus, the propensity ratio ratio, but not on government resources.
depends
on
the
relative
price
and
the
A. Razin.
Integrared
world
stock marker
115
straints [eqs. (1) and (2)] we derive consumption and asset demands as functions of security prices, 4 and q *, the entire distribution of second-period taxes, {T, 1, and the level of wealth, W,,. The demand functions are: ZHl CHO=CHOCqrq*,{Tl~;W01~
= zHl [q,
q*v {Tll ,; WIJI,
and zg, =zz, [q, q*, {T, f; W,]. Wealth, defined by w0=(q+&,)zH0+(q*
+@)zi&-
7-0,
(9)
is a function of q, q* and 7’,. The foreign private sector (indicated by subscript F) solves essentially a similar problem. The model is closed by the world market-clearing conditions for current-period consumption and equities of firms located in each one of the two countries. World equilibrium is:
(10)
ZB,cq, q*,{Tl)?W,l = y:.
(12)
As usual, by Walras’ law one of the equilibrium conditions is redundant. Accordingly, we choose to omit the current-consumption market-clearing condition, eq. (lo), from the analysis. The remaining equilibrium conditions in eqs. (11) and (12) are then used to solve for the market-clearing prices q and q*. In the absence of uncertainty, all assets are perfect substitutes with a single rate of return, i.e. the rate of interest. Recall [see Frenkel and Razin (1987b)] that the effect of government spending on the rate of interest is governed by a simple transfer-problem criterion. Define consumer wealth as Z,r,( Y,- T,) and its saving as the discounted flow of future consumption, ZlrlC,, where a, is the present value factor. Similarly, define government ‘wealth’ by G= E,,a,G,, and the discounted flow of its future spending by E,r,G, as the government ‘savings’. If the marginal propensity to save out of wealth by the home country private sector exceeds the corresponding saving propensity of the home country government, the world interest rate, linking the present to the future, must rise with the increase in government spending (since the rise in government spending and taxes amounts to a transfer from the high saver - the private sector - to the low saver - the government), and vice versa. In the presence of uncertainty, however, assets are imperfect substitutes and the returns on different assets need not be equal to the rate of interest. The nature of the world equilibrium, characterized by free financial capital movements, could be analyzed with the aid of fig. 2. The upward-sloping
116
A. Razin, Integrated world stock market Lo9
d
Lo9
9’
Log q-
Lo9 4’ Fig. 2. The ekt
of a transitory
Lo9 9
Lo9 q
balanced-budget
rise in current
government
spending.
schedule, 22, describes different combinations of the security prices q and q* which clear the domestic-asset market. Likewise, the upward-sloping schedule Z*Z* describes different combinations of prices q and q* which clear the foreign-security market. A useful benchmark case for the analysis is the one in which the portfolio composition does not change over time (analogously to the stationary state in the infinite-horizon problem). Observe that income effects associated with price changes vanish and there remain substitution effects only. Accordingly, zH1
=
ZHO~
*-*
zH1
-zHO,
zFI
=
zFO
and
z& = zgo.
Around such an equilibrium point the ZZ schedule is steeper than the Z*Z* schedule. To verify, we differentiate eqs. (11) and (12) by using the definition of wealth given in eq. (9). Rearranging, and making use of the Slutsky decomposition, yields: dlogq*_
dlogq
~Z;ilq-~ZH1-ZHO~ZH1~~+~z~lq-~ZF1-ZFO~Z~lW~
[~Kr~.--(ztfit -z* HO )z HlWl
+[zs-lqdz:l
-a-ZFO)ZFIW1
q*
(13)
4
along the ZZ schedule, and
along the Z*Z* schedule, where a subscript denotes partial derivatives (e.g. and a superscript s indicates that the price effect applies to
azHl/dq~zHlq)
A. Ra:in,
Integrated
world
stock
market
117
the compensated asset demand. In the appendix I derive the following elementary properties for the asset-demand functions:
z;,,
ZJlq.=Zj:lq>O,
q*zj,,* < -q&q,
zj:‘,.
qzi:“, < - q*zj:lq.,
j = H, F.
That is to say, with the time separable utility function, assets z and z* are net substitutes and the own elasticity is larger (in absolute value) than the cross elasticity. Combining these properties of asset-demand functions with the right-hand sides of eqs. (13) and (14), and evaluating at the stationary-portfolio equilibrium point (the benchmark case), it is seen that the ZZ and Z*Z* schedules are upward-sloping, and that the former schedule is steeper than the latter. Consider the initial equilibrium point A in fig. 2. A rise in the domesticsecurity price, due to substitution effects, generates an excess supply of domestic securities and an excess demand for foreign securities. To restore equilibrium in the market for foreign securities, the foreign security price, q*, must rise. Similarly, to clear the domestic-security market the foreign country price, q*, must rise proportionally more, since the changes in q have larger effects on the demand for domestic securities than on foreign securities. The converse is true with regard to changes in q*. Consider now the effect of a current period transitory rise in the home country’s government spending. The rise in current government spending (associated with a corresponding tax hike) creates an excess supply of domestic securities and necessitates a corresponding rise in private-sector demand. As implied by eq. (3), the ZZ schedule shifts to the left, to Z’Z’. The same rise in government spending creates also an excess supply of foreign securities and necessitates a corresponding increase in demand that is reflected by a downward shift of the schedule from Z*Z* to Z*‘Z*‘. Thus, the prices of domestic and foreign securities must fall. This obviously conforms with the results of the nonstochastic analysis [see Frenkel and Razin (1987b)] in which a transitory rise in government spending raises the equilibrium world rate of interest. Analogously, in the present case expected yields on both assets rise. Consider now the effect of a stochastic future rise in the home country’s government spending. Since the future becomes relatively scarce, it is more highly valued. As a result, consumption falls while savings rise. In other words, through the consumption-smoothing mechanism the fall in future disposable income enhances current-period savings. But even though the demand for assets as a group rises, we cannot ascertain that the demand for each and every asset necessarily rises. Thus, we need more information about
118
A. Razin, Integrated
world stock market
the parameters of the demand functions and the correlations between the stochastic returns to evaluate such effects. This is done in the next section.
6. Spending policies and the CAPM valuation The roles played by the correlations of government spending and asset returns are conveniently analyzed in the case of CAPM equilibrium valuations. We turn here to this specification and maintain the assumption of a balanced government budget, state by state. Let there be a safe tradable bond with a return, R,. Incorporating into the consolidated budget constraint, the relation between future consumption and current consumption is given by:
C,,(Y)= ~o-GI(Y)--RoCH,+(8,(y)--Rodz,, +(WJ)--oq*M, where IV, is defined as in eq. (9). Assume that 8,(y) and O:(y) are normally distributed and let the private component of the expected utility function be:
z-e
- bCno
_
ae-
b[ECH,(lj-(b/Z)var(C~*(Y))l 3
(15)
where b is the constant absolute risk-aversion parameter and var( *) denotes the variance. Adding the individual country first-order conditions to each other yields:
(16)
* _ y: 4--
-~wwd
y:, C,,(Y)+ c,,b9) Roy:
9
(17)
where B = l/[( l/b) +( l/b*)] is the world market risk-aversion coefficient. Using the equilibrium condition CH1 + C,, + G = 0: Y: + O1Y,, the covariance terms can be expressed explicitly as follows:
A. Razin, Integrated
119
world stock market
cov(~t(;1)Yt,C,,(~)+CFI(Y))= y:%l+ Y:o,,.- Y,a,,, and
cov(wt9y*,,
cIi,b)+G,(Y))=
yt yrfJ,,*+ yr2%w- y:%G
where ox,, denotes the covariance between x and y. The equation characterizing R,-, (derived similarly from the first-order conditions and the equilibrium condition) is:
;logR,=(Y,+
Y:-EC,(y))-(Ye+
Y,*)-
;log6++Jog6* >
. -~BCY:a,B+2Y,Y:ae,*+Y:2a,*,.]+tB(Y:bgG+Y,(rec). (18)
It is evident from the equilibrium-valuation conditions in eqs. (16)-(18) that as long as the average level of government spending, EC,(y), remains constant, a change in the distribution of government spending across states raises or lowers the equilibrium prices of equities, 4 and q*, according to whether the covariances crBGand c,.,.~ are positive or negative, respectively. Thus, a procyclical policy generating a positive correlation between government spending and productivity in the domestic industry raises the stock-market value of the industry and raises the rate of interest. Analogously, a positive correlation between government spending and productivity in the foreign industry raises the industry stock-market value and raises the rate of interest.
Thus, the correlation between marginal changes in government spending and the country-specitic productivity shocks fully determine the effects of the fiscal policy on the equilibrium valuations in the integrated world stock market.3
7. Concluding remarks This paper extends the analysis of the effects of fiscal policies on the world equilibrium to uncertain environments in which the key channel of transmission is the world stock market. The analysis shows that if the statecontingent marginal propensity to spend by the government exceeds the corresponding domestic private-sector propensity, the equilibrium statecontingent price must rise. As a result, the domestic equity price rises relative to the foreign equity price if the domestic economy is relatively more ‘Similar
patterns
are indicated
in Flood
(1988).
120
A. Razin, Integrated
world stock market
productive in this state in comparison with the foreign economy, and vice versa. Whether equity prices, in terms of current-period consumption, rise or fall depends both on the means of government finance and on the crosscountry productivity correlations.
Appendix: Characteristics of asset demands In this appendix we derive the key characteristics of the asset-demand functions which underlie the slopes of the schedules ZZ and Z*Z* in fig. 2. To simplify the notation we suppress all period and country subscripts. Using eqs. (2) and (3) the private component of the utility function can be expressed as a function of Co, z, z* and {T,(y)} as follows:
=
u(C,) + 4z, z*,Tl (Y)).
(19)
Consider the inverse of the function u(C,), that is, C,=u-r(u) = 4(u), the expenditure function p(q, q*, {T,(y)), u) associated with u(z, z*, {Tr (y)}), and the expenditure function m[l,q,q*,{T, (y)), U] associated with U(C,, z, z*, (T,(y)}). They are related to each other as follows: min{l~f$(u)+~(q,q*,{T,(y)),u) mC4q,q*,{~l(;1)},Ul=
s.t.u+o=UJ
Y.”
=minCl *4(U -
u) +p(q, q*, {T,(y)}, 141.
(20)
”
The first-order condition of the optimization
problem in (20) is:
As usual, the compensated-asset demands are the partial derivatives of the expenditure function (20) with respect to prices (l,q,q*). To obtain explicit expressions for ut, up, and uP, we differentiate the first-order condition, which yields:
Substituting yields:
these expressions
into the second-order
derivatives
of m(a)
A. Razin, Integrated
world stock market
121
and
The negative sign of mq4 follows from the fact that pqqpqV~,&, and from the fact that since pq( .) is homogeneous of degree zero in (4, q*), and pLp,,is negative, pq is positive. Thus, @‘pqq.>O. The condition rnql >O implies that the domestic security demand is negatively related to q, and the condition mqq,>O implies that the assets z and z* are net substitutes.
Multiplying the expression for mq4 by q and adding to the expression of mqq., multiplied by q*, yields:
(21) where use has been made of the familiar properties of the expenditure function that: (1) cl,, is homogeneous of degree zero in the prices q and q*, and (2) JL”is homogeneous of degree one in these prices. The negative sign of (21) implies that q*~+~< -qmqp. This means that a rise in the domestic security price, q, exerts a more pronounced effect on the demand for this security than on the demand for the other security. Similarly, it can be verified that a rise in q* exerts a weaker effect on z’ than on z*‘.
Barro, R.J., 1981, Output effects of government purchases, Journal of Political Economy 89, 10861121. Blanchard, O.J., 1985, Debt, deficits and finite horizons, Journal of Political Economy 93, 223-247. Buiter, W., 1986, Structural and stabilization aspects of fiscal and financial policies in the dependent economy, Part I, Unpublished manuscript, Macroeconomic Division, DRD, the World Bank. Diamond, P.A., 1967, The role of a stock market in a general equilibrium model with technological uncertainty, American Economic Review 57, 759-776. Flood, R.P.,-1988, Asset prices and time-varying risk, IMF. Frenkel. J.A. and A. Razin, 1985, Government spending, debt and international economic interdependence, Economic Journal 95, 619639.
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stock market
Frenkel, J.A. and A. Razin, 1987a. Spending, taxes and real exchange rates, Unpublished manuscript, Research Department. IMF. Frenkel, J.A. and A. Razin, 1987b, Fiscal policies and the world economy: An intertemporal approach (MIT Press, Cambridge, MA). Helpman, E. and A. Razin, 1978, A theory of international trade under uncertainty (Academic Press, New York). Lucas, R.E., Jr., 1978, Asset prices in an exchange economy, Econometrica 46, 1429-14-U. Persson, T., 1985, Deficits and intergenerational welfare in open economies, Journal of International Economics 19, 1-19. Svensson, L.E.O., 1988, Trade in risky assets, American Economic Review 78.
Economics 29 (1990) 109-122. North-Holland
FISCAL POLICIES
AND THE INTEGRATED MARKET
WORLD
STOCK
Assaf RAZIN* Tel-Aviv Unicersity, Tel Aviv 69978. Israel
Received September 1988, revised version received December 1989 The paper develops a two-country stochastic model of an integrated world stock market in order to address issues concerning the effects of tax and spending policies on savings, asset portfolios, and stock-market valuations. General conditions for government-finance neutrality under uncertainty are derived and the characteristics of the international transmission of uncertain future spending policies are spelled out. They are shown to depend precisely on a transfer-problem criterion involving the government and the private-sector propensities to spend in different states of nature and on the cross-country correlations between shocks to productivity and public spending.
1. Introduction
This paper develops a two-country stochastic general-equilibrium model of the world economy to address issues concerning the effects of fiscal policies on the international allocation of consumption, saving, and risk. The analytical framework is used to study the effects of government spending and tax policies on private-sector consumption, spending, and asset portfolios. The recent large swings in security prices that have taken place simultaneously throughout the OECD stock markets indicate the close international links existing among various stocks as a result of the integration of the world capital markets. They motivate the assumption of an integrated world stock market. The dynamic effects of fiscal policies on savings and investment have been the subject of a large body of recent research. Examples of such research in a closed-economy framework are Barro (1981) and Blanchard (1985), and examples in an open-economy framework are Buiter (1986), Frenkel and Razin (1985, 1987a, 1987b) and Persson (1985). This line of research, emphasizing intertemporal considerations, has been confined, however, to a full-certainty environment in which private-sector behavior is governed by *This is a revision of the NBER working paper no. 2398 (1987). I wish to thank Elhanan Helpman, Torsten Persson and Lars Svensson for useful comments. Partial tinancial support was provided by the Foerder Institute for Economic Research, Tel-Aviv University. 0022-1996/90/$03.50 0 1990-Elsevier
Science Publishers B.V. (North-Holland)
110
A. hrin,
integrated
world sock market
perfect foresight. The open-economy macroeconomic analysis under certainty focused mainly on the international and intertemporal allocation of consumption and investment and their manifestations in trade imbalances. In such a framework the terms of trade and the world rate of interest are the main channels through which fiscal policies in one country are transmitted to the rest of the world. The present paper extends the analysis to stochastic environments in which the main channel of transmission is the integrated world stock market. The extension of the international-intertemporal framework to stochastic environments is done here by specifying a stock-market model as in Diamond (1967), Helpman and Razin (1978) and Lucas (1978). A recent application of the model to international trade in assets is contained in Svensson (1988). The paper is organized in the following manner. In section 2 we set out the stochastic-intertemporal analytical framework. Section 3 considers the issue of the government-finance neutrality and section 4 contains the analysis of spending policies in the case of complete markets for risk sharing. In the context of incomplete markets, sections 5 and 6 investigate how the pro- and counter-cyclical behavior of government spending affects the stock market valuation of equities. The analysis highlights the role played by the correlations between the country-specific shocks and government spending shocks in the international transmission of fiscal policies. Section 7 contains concluding remarks. The appendix, which follows the text, includes algebraic derivations of the key characteristics of the asset-demand functions under uncertainty. 2. An intertemporal
stochastic model
Consider a two-period nonmonetary model of an open economy producing and consuming a single aggregate tradable good.’ The economy is endowed with a sequence of outputs, O,Y,, and B,(y) Y,, where subscripts zero and one designate the corresponding periods indexed by the state of nature, y. There are S possible states of nature, the quantities O,Y, and Y, are predetermined, and O,(y) is a productivity coefficient corresponding to the state of technology, ~=1,2 ,..., S. Similarly to Helpman and Razin (1978), let q be the price of a unit of real equity [a security which pays O(y) units of output in state 71 issued by the representative home firm, in terms of units of the aggregate consumption good. Home firms produce Yi units of these equities and their (gross) stock market value is equal to q- Y,. An asterisk denotes foreign variables. Accordingly, foreign firms produce the sequence O,*Y,*and O:(y) YT in periods zero and one, respectively; the price of a unit of foreign ‘The present model is a two-period one-good version of the model developed by Helpman and Razin (1978, ch. 11). Labor income is contained in the endowment BY. Fixed return bonds are introduced later, in section 5.
A. Razin, lntegrated
world stock market
111
real equity is denoted by q* and the stock-market value of foreign firms is equal to q* . YT. The domestic private-sector budget constraints are: &0 + q2,,l + qz;ci = qz,,, + q*z;O
+
oOzHO
+
@z;l;O
-
rO,
c”l(‘r’)=el(Y)zH1 +e:(;t)ztl - Tl(‘i).
(1)
(2)
In eqs. (1) and (2), CHOand C,,(y) denote first- and (state-y) second-period consumption and zHr and z& denote the shares of stocks issued by home and foreign firms in period t (t=O, 1). The productivity parameters, 8, and OF, indicate the amount of dividends, per share, paid by domestic and foreign firms, respectively, and T, denotes lump-sum taxes in period t (t = 0,l). In eq. (1) disposable income is equal to current dividends from the historically given portfolio (zno, z*no), plus the market value of this portfolio net of taxes, To. Income is spent on consumption, CHO, and on the new portfolio, (z H1,z;cIi). Second-period disposable income, specified in eq. (2), is derived from dividends on the pre-existing portfolio (net of taxes), but includes no resale value of stocks and no acquisition of new stocks, since this is the last period. Let u(C,,) and M(G,) be concave von Neumann-Morgenstern private and public components of the representative individual utility function, respectively, and let 6 denote the corresponding subjective discount factor. The expected utility is:
u=4&o)
+
~EuCCHI
(r)l+ WGo) + dEM(G, (Y)),
(3)
where E is the expectation operator. The consumption-portfolio choice problem is to maximize the private component of the expected utility function [eq. (3)], given common beliefs about the probability distribution of states of nature and subject to the budget constraints [eqs. (1) and (2)]. Given its own resources (through taxes and borrowing), G, the government, chooses Go and G, so as to maximize the public component of the expected utility function.
3. Neutrality of government finance To put aside issues of government finance and concentrate on spending policies in the subsequent analysis, we specify in this section conditions for a benchmark case in which government finance has no real consequence. Observe that the consolidated private-sector budget constraint [derived from eqs. (1) and (2)] is:
112
A. Razin, Integrated
It is evident
maintains the return on what may be called the ‘tax asset’ (the claim of government on private sector income) are proportional to the returns on the domestic security, state by state. Thus, the government finance activities effectively introduce no new security into the market. Simply stated, the government raises current-period taxes and use the proceeds to buy domestic equities, while in the next period state-dependent dividend revenue replaces taxes as a source of government finance. These financial transactions have no effect on the private sector. Conditions for government-finance neutrality can be stated as a proposition: (-)T,(y)/T,,
from
eq. (4) that
world stock market
any
tax-shift
policy
that
=O,(y)/q must be neutral. If tax policies fulfill this condition,
Proposition. The claim of the private sector on taxes can be viewed as a negative ‘asset’. Whether or not tax-shift policies are relevant depends on whether the induced distribution of returns on this ‘asset’ is spanned by the equilibrium returns on the prevailing assets.
4. Spending, international allocation of risk, and stock price valuations To highlight the effects of government spending on the international allocation of risk, and specifically on the relative price of the domestic security (in terms of the foreign security), we assume now that markets are complete. In the present context, since there are only two securities, this assumption implies that there exist two states of nature (0 and 1). Maximization of the private component of the expected utility yields: R(o)u’(o)e*(o) + K(l)u’( l)e*( 1) -* n(o)u’(o)e(o) + n( l)u’( l)e( 1)
’
(5)
where 4* is the relative price of the foreign security in terms of the domestic security. We denote the ratio of the price of a state-one contingent good, P,, to a state-zero contingent good, P,, by p. Then, as usual, in equilibrium the marginal rate of substitution is equal to the relative price. That is,
MU’
---c
?r(O)u’(O) p.
Eqs. (5) and (6) imply the following relationship between p and 4*:
(6)
A. Razin, lntegrated
world
stock market
,rlopc
1 AG(l)
=
.IPG(l)/MPG(O)
B(l)Y+ Z(l)Y.
OH
/
”
stopen
MPC(l)/MPC(O),
Fig. 1. The effect of a rise in government
e*(o)+Pe*u)=q_* w+Pf%l)
’
ll(O)Y
+ O’(O)Y’
spending
on the relative state-contingent
price.
(7)
Accordingly,
(8)
Similar conditions, with the same prices, hold for the foreign country. The equilibrium in the world economy is portrayed by the Edgeworth box in fig. 1. The horizontal axis measures world output in state zero [e(O) Y +0*(O) Y*] and the vertical axis measures the corresponding output in state one [0( l)Y+ 0*( l)Y*]. The international distribution of claims to world output is specified by the point E. As usual, quantities pertaining to the home country are measured from the point OH as the origin, and quantities pertaining to the foreign country are measures from point OF as the origin. The equilibrium obtains at point A, where the slope of the domestic and foreign indifference curves are both equal to the relative price, p. Using eq. (7) we can also derive the equilibrium relative price of the foreign security, $+.
114
A. Razin,
Integrated
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stock market
The government propensity to spend in the first and second states is determined by maximizing the public component of the expected utility function, M(G0)+6~(0)-M(G,(O))+&( l)M(G,( l)), subject to the budget constraint G,+P,,G,(O)+P,G,( l)=G, where G denotes the present value of the tax revenue. Optimization yields the endogenously determined propensities to spend for the government, which depend on the probabilities (the x’s), on the relative price (p), and on the government resources (G).’ As in Frenkel and Razin (1987b), the basic criterion determining the effect of a rise in government spending on the relative price of goods involves a comparison between the ratio of government marginal propensities to spend, MPG(l)/MPG(O) [where MPG(i) is the government propensity to spend in state i] and the corresponding ratio of the domestic private sector propensities to consume, MPC(l)/MPC(O) [where MPC(i) denotes the privatesector marginal propensity in state i]. If the government propensity to spend exceeds the private-sector propensity to consume in state one, the rise in government spending and the corresponding fall in the disposable income of the domestic private sector create an excess demand for state-one goods and an excess supply of state-zero goods. As a result p rises. If, on the other hand, the government propensity falls short of the corresponding privatesector propensity, the equilibrium relative price, p, must fall. This is indicated in fig. 1 by the diminished size of the box. In the borderline case which is shown in the figure, the relative propensities of the public and the private sectors are equal. The new equilibrium following the rise in government spending obtains at point B with no change in marketclearing prices. In this case there is no change in the relative price of the domestic security [see eq. (8)]. However, if the public-private propensity configuration is such that state-
one relative price, p, goes up, and if the domestic economy is relatively more productive in that state, the relative price of the domestic security must rise [as indicated by eq. (8)] and vice versa.
5. Spending and international allocation of risk with incomplete markets To highlight the effects of spending policies in the case of incomplete markets we abstract now from issues of government finance assuming that the government runs a balanced budget [G,= T,, G,(y) = T,(y)]. From the maximization of the expected utility [eq. (3)] subject to the budget con-
‘If, for example, the utility function is logarithmic, the ratio of the marginal propensity to spend in state one to the corresponding propensity in state zero, [~G,(~)/c~G]/[X,(O)/ZG], is equal to probability
[n(i)/x(O)p]. Thus, the propensity ratio ratio, but not on government resources.
depends
on
the
relative
price
and
the
A. Razin.
Integrared
world
stock marker
115
straints [eqs. (1) and (2)] we derive consumption and asset demands as functions of security prices, 4 and q *, the entire distribution of second-period taxes, {T, 1, and the level of wealth, W,,. The demand functions are: ZHl CHO=CHOCqrq*,{Tl~;W01~
= zHl [q,
q*v {Tll ,; WIJI,
and zg, =zz, [q, q*, {T, f; W,]. Wealth, defined by w0=(q+&,)zH0+(q*
+@)zi&-
7-0,
(9)
is a function of q, q* and 7’,. The foreign private sector (indicated by subscript F) solves essentially a similar problem. The model is closed by the world market-clearing conditions for current-period consumption and equities of firms located in each one of the two countries. World equilibrium is:
(10)
ZB,cq, q*,{Tl)?W,l = y:.
(12)
As usual, by Walras’ law one of the equilibrium conditions is redundant. Accordingly, we choose to omit the current-consumption market-clearing condition, eq. (lo), from the analysis. The remaining equilibrium conditions in eqs. (11) and (12) are then used to solve for the market-clearing prices q and q*. In the absence of uncertainty, all assets are perfect substitutes with a single rate of return, i.e. the rate of interest. Recall [see Frenkel and Razin (1987b)] that the effect of government spending on the rate of interest is governed by a simple transfer-problem criterion. Define consumer wealth as Z,r,( Y,- T,) and its saving as the discounted flow of future consumption, ZlrlC,, where a, is the present value factor. Similarly, define government ‘wealth’ by G= E,,a,G,, and the discounted flow of its future spending by E,r,G, as the government ‘savings’. If the marginal propensity to save out of wealth by the home country private sector exceeds the corresponding saving propensity of the home country government, the world interest rate, linking the present to the future, must rise with the increase in government spending (since the rise in government spending and taxes amounts to a transfer from the high saver - the private sector - to the low saver - the government), and vice versa. In the presence of uncertainty, however, assets are imperfect substitutes and the returns on different assets need not be equal to the rate of interest. The nature of the world equilibrium, characterized by free financial capital movements, could be analyzed with the aid of fig. 2. The upward-sloping
116
A. Razin, Integrated world stock market Lo9
d
Lo9
9’
Log q-
Lo9 4’ Fig. 2. The ekt
of a transitory
Lo9 9
Lo9 q
balanced-budget
rise in current
government
spending.
schedule, 22, describes different combinations of the security prices q and q* which clear the domestic-asset market. Likewise, the upward-sloping schedule Z*Z* describes different combinations of prices q and q* which clear the foreign-security market. A useful benchmark case for the analysis is the one in which the portfolio composition does not change over time (analogously to the stationary state in the infinite-horizon problem). Observe that income effects associated with price changes vanish and there remain substitution effects only. Accordingly, zH1
=
ZHO~
*-*
zH1
-zHO,
zFI
=
zFO
and
z& = zgo.
Around such an equilibrium point the ZZ schedule is steeper than the Z*Z* schedule. To verify, we differentiate eqs. (11) and (12) by using the definition of wealth given in eq. (9). Rearranging, and making use of the Slutsky decomposition, yields: dlogq*_
dlogq
~Z;ilq-~ZH1-ZHO~ZH1~~+~z~lq-~ZF1-ZFO~Z~lW~
[~Kr~.--(ztfit -z* HO )z HlWl
+[zs-lqdz:l
-a-ZFO)ZFIW1
q*
(13)
4
along the ZZ schedule, and
along the Z*Z* schedule, where a subscript denotes partial derivatives (e.g. and a superscript s indicates that the price effect applies to
azHl/dq~zHlq)
A. Ra:in,
Integrated
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stock
market
117
the compensated asset demand. In the appendix I derive the following elementary properties for the asset-demand functions:
z;,,
ZJlq.=Zj:lq>O,
q*zj,,* < -q&q,
zj:‘,.
qzi:“, < - q*zj:lq.,
j = H, F.
That is to say, with the time separable utility function, assets z and z* are net substitutes and the own elasticity is larger (in absolute value) than the cross elasticity. Combining these properties of asset-demand functions with the right-hand sides of eqs. (13) and (14), and evaluating at the stationary-portfolio equilibrium point (the benchmark case), it is seen that the ZZ and Z*Z* schedules are upward-sloping, and that the former schedule is steeper than the latter. Consider the initial equilibrium point A in fig. 2. A rise in the domesticsecurity price, due to substitution effects, generates an excess supply of domestic securities and an excess demand for foreign securities. To restore equilibrium in the market for foreign securities, the foreign security price, q*, must rise. Similarly, to clear the domestic-security market the foreign country price, q*, must rise proportionally more, since the changes in q have larger effects on the demand for domestic securities than on foreign securities. The converse is true with regard to changes in q*. Consider now the effect of a current period transitory rise in the home country’s government spending. The rise in current government spending (associated with a corresponding tax hike) creates an excess supply of domestic securities and necessitates a corresponding rise in private-sector demand. As implied by eq. (3), the ZZ schedule shifts to the left, to Z’Z’. The same rise in government spending creates also an excess supply of foreign securities and necessitates a corresponding increase in demand that is reflected by a downward shift of the schedule from Z*Z* to Z*‘Z*‘. Thus, the prices of domestic and foreign securities must fall. This obviously conforms with the results of the nonstochastic analysis [see Frenkel and Razin (1987b)] in which a transitory rise in government spending raises the equilibrium world rate of interest. Analogously, in the present case expected yields on both assets rise. Consider now the effect of a stochastic future rise in the home country’s government spending. Since the future becomes relatively scarce, it is more highly valued. As a result, consumption falls while savings rise. In other words, through the consumption-smoothing mechanism the fall in future disposable income enhances current-period savings. But even though the demand for assets as a group rises, we cannot ascertain that the demand for each and every asset necessarily rises. Thus, we need more information about
118
A. Razin, Integrated
world stock market
the parameters of the demand functions and the correlations between the stochastic returns to evaluate such effects. This is done in the next section.
6. Spending policies and the CAPM valuation The roles played by the correlations of government spending and asset returns are conveniently analyzed in the case of CAPM equilibrium valuations. We turn here to this specification and maintain the assumption of a balanced government budget, state by state. Let there be a safe tradable bond with a return, R,. Incorporating into the consolidated budget constraint, the relation between future consumption and current consumption is given by:
C,,(Y)= ~o-GI(Y)--RoCH,+(8,(y)--Rodz,, +(WJ)--oq*M, where IV, is defined as in eq. (9). Assume that 8,(y) and O:(y) are normally distributed and let the private component of the expected utility function be:
z-e
- bCno
_
ae-
b[ECH,(lj-(b/Z)var(C~*(Y))l 3
(15)
where b is the constant absolute risk-aversion parameter and var( *) denotes the variance. Adding the individual country first-order conditions to each other yields:
(16)
* _ y: 4--
-~wwd
y:, C,,(Y)+ c,,b9) Roy:
9
(17)
where B = l/[( l/b) +( l/b*)] is the world market risk-aversion coefficient. Using the equilibrium condition CH1 + C,, + G = 0: Y: + O1Y,, the covariance terms can be expressed explicitly as follows:
A. Razin, Integrated
119
world stock market
cov(~t(;1)Yt,C,,(~)+CFI(Y))= y:%l+ Y:o,,.- Y,a,,, and
cov(wt9y*,,
cIi,b)+G,(Y))=
yt yrfJ,,*+ yr2%w- y:%G
where ox,, denotes the covariance between x and y. The equation characterizing R,-, (derived similarly from the first-order conditions and the equilibrium condition) is:
;logR,=(Y,+
Y:-EC,(y))-(Ye+
Y,*)-
;log6++Jog6* >
. -~BCY:a,B+2Y,Y:ae,*+Y:2a,*,.]+tB(Y:bgG+Y,(rec). (18)
It is evident from the equilibrium-valuation conditions in eqs. (16)-(18) that as long as the average level of government spending, EC,(y), remains constant, a change in the distribution of government spending across states raises or lowers the equilibrium prices of equities, 4 and q*, according to whether the covariances crBGand c,.,.~ are positive or negative, respectively. Thus, a procyclical policy generating a positive correlation between government spending and productivity in the domestic industry raises the stock-market value of the industry and raises the rate of interest. Analogously, a positive correlation between government spending and productivity in the foreign industry raises the industry stock-market value and raises the rate of interest.
Thus, the correlation between marginal changes in government spending and the country-specitic productivity shocks fully determine the effects of the fiscal policy on the equilibrium valuations in the integrated world stock market.3
7. Concluding remarks This paper extends the analysis of the effects of fiscal policies on the world equilibrium to uncertain environments in which the key channel of transmission is the world stock market. The analysis shows that if the statecontingent marginal propensity to spend by the government exceeds the corresponding domestic private-sector propensity, the equilibrium statecontingent price must rise. As a result, the domestic equity price rises relative to the foreign equity price if the domestic economy is relatively more ‘Similar
patterns
are indicated
in Flood
(1988).
120
A. Razin, Integrated
world stock market
productive in this state in comparison with the foreign economy, and vice versa. Whether equity prices, in terms of current-period consumption, rise or fall depends both on the means of government finance and on the crosscountry productivity correlations.
Appendix: Characteristics of asset demands In this appendix we derive the key characteristics of the asset-demand functions which underlie the slopes of the schedules ZZ and Z*Z* in fig. 2. To simplify the notation we suppress all period and country subscripts. Using eqs. (2) and (3) the private component of the utility function can be expressed as a function of Co, z, z* and {T,(y)} as follows:
=
u(C,) + 4z, z*,Tl (Y)).
(19)
Consider the inverse of the function u(C,), that is, C,=u-r(u) = 4(u), the expenditure function p(q, q*, {T,(y)), u) associated with u(z, z*, {Tr (y)}), and the expenditure function m[l,q,q*,{T, (y)), U] associated with U(C,, z, z*, (T,(y)}). They are related to each other as follows: min{l~f$(u)+~(q,q*,{T,(y)),u) mC4q,q*,{~l(;1)},Ul=
s.t.u+o=UJ
Y.”
=minCl *4(U -
u) +p(q, q*, {T,(y)}, 141.
(20)
”
The first-order condition of the optimization
problem in (20) is:
As usual, the compensated-asset demands are the partial derivatives of the expenditure function (20) with respect to prices (l,q,q*). To obtain explicit expressions for ut, up, and uP, we differentiate the first-order condition, which yields:
Substituting yields:
these expressions
into the second-order
derivatives
of m(a)
A. Razin, Integrated
world stock market
121
and
The negative sign of mq4 follows from the fact that pqq
Multiplying the expression for mq4 by q and adding to the expression of mqq., multiplied by q*, yields:
(21) where use has been made of the familiar properties of the expenditure function that: (1) cl,, is homogeneous of degree zero in the prices q and q*, and (2) JL”is homogeneous of degree one in these prices. The negative sign of (21) implies that q*~+~< -qmqp. This means that a rise in the domestic security price, q, exerts a more pronounced effect on the demand for this security than on the demand for the other security. Similarly, it can be verified that a rise in q* exerts a weaker effect on z’ than on z*‘.
Barro, R.J., 1981, Output effects of government purchases, Journal of Political Economy 89, 10861121. Blanchard, O.J., 1985, Debt, deficits and finite horizons, Journal of Political Economy 93, 223-247. Buiter, W., 1986, Structural and stabilization aspects of fiscal and financial policies in the dependent economy, Part I, Unpublished manuscript, Macroeconomic Division, DRD, the World Bank. Diamond, P.A., 1967, The role of a stock market in a general equilibrium model with technological uncertainty, American Economic Review 57, 759-776. Flood, R.P.,-1988, Asset prices and time-varying risk, IMF. Frenkel. J.A. and A. Razin, 1985, Government spending, debt and international economic interdependence, Economic Journal 95, 619639.
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stock market
Frenkel, J.A. and A. Razin, 1987a. Spending, taxes and real exchange rates, Unpublished manuscript, Research Department. IMF. Frenkel, J.A. and A. Razin, 1987b, Fiscal policies and the world economy: An intertemporal approach (MIT Press, Cambridge, MA). Helpman, E. and A. Razin, 1978, A theory of international trade under uncertainty (Academic Press, New York). Lucas, R.E., Jr., 1978, Asset prices in an exchange economy, Econometrica 46, 1429-14-U. Persson, T., 1985, Deficits and intergenerational welfare in open economies, Journal of International Economics 19, 1-19. Svensson, L.E.O., 1988, Trade in risky assets, American Economic Review 78.